Q: What are the factor combinations of the number 104,005,223?

 A:
Positive:   1 x 1040052237 x 1485788929 x 3586387131 x 793933203 x 512341917 x 1134193799 x 273773911 x 26593
Negative: -1 x -104005223-7 x -14857889-29 x -3586387-131 x -793933-203 x -512341-917 x -113419-3799 x -27377-3911 x -26593


How do I find the factor combinations of the number 104,005,223?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 104,005,223, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 104,005,223
-1 -104,005,223

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 104,005,223.

Example:
1 x 104,005,223 = 104,005,223
and
-1 x -104,005,223 = 104,005,223
Notice both answers equal 104,005,223

With that explanation out of the way, let's continue. Next, we take the number 104,005,223 and divide it by 2:

104,005,223 ÷ 2 = 52,002,611.5

If the quotient is a whole number, then 2 and 52,002,611.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 104,005,223
-1 -104,005,223

Now, we try dividing 104,005,223 by 3:

104,005,223 ÷ 3 = 34,668,407.6667

If the quotient is a whole number, then 3 and 34,668,407.6667 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 104,005,223
-1 -104,005,223

Let's try dividing by 4:

104,005,223 ÷ 4 = 26,001,305.75

If the quotient is a whole number, then 4 and 26,001,305.75 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 104,005,223
-1 104,005,223
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

17291312039173,7993,91126,59327,377113,419512,341793,9333,586,38714,857,889104,005,223
-1-7-29-131-203-917-3,799-3,911-26,593-27,377-113,419-512,341-793,933-3,586,387-14,857,889-104,005,223

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